You are driving your 6 cylinder vehicle down the highway at

You are driving your 6 cylinder vehicle down the highway at a constant speed of 80.0 mph. You do this for 60.0 minutes using your cruise control so that the speed does not vary at all (obviously you are on a flat stretch of road with no construction). The tachometer in your vehicle says that your engine is running at 1800. rpm for the entire time and does not vary (not very realistic but it makes the math easier). Your super fancy dashboard computer says that your vehicle is getting a consistent 28 miles per gallon.

Your engine is a 4 stroke engine in which the pistons do the following (kindergarten level auto mechanics): (1) piston is at the bottom and as it goes up the cylinder, fuel and air are injected into the cylinder and at the top of the cylinder the spark plug fires and ignites the fuel air mixture. (2) the force of the explosion forces the piston down the cylinder which turns the crankshaft which drives your car down the road, (3) the piston rises to the top of the cylinder but does NOT receive additional fuel , (4) the piston travels down the cylinder and the residual gases from the cylinder are exhausted from the piston and do down the tail pipe to the muffler. Steps 1 and 2 constitute one revolution and steps 3 and 4 constitute a second revolution as measured by the tachometer.

So, here is the question. How many drops of gasoline are injected into EACH cylinder during step (1) as outlined above. Assume that 1.00 mL of gasoline is equal to 20. drops.

Can you please show how to solve this?

Solution

Answer:

Speed of the vehicle = 80 mile/h = 80/60 mile/minute

Distance covered in 60 minutes = 60 x 80/60 = 80 miles

Total gallon consumed in covering 80 miles = 80/28 = 2.85 gallon

1800 rpm taken to distance = 80 mles

1 rpm = 80/1800 = 0.044 mile

Now for 80 miles the vehicle the fuel taken = 2.85 gallon

0.044 miles .... = 2.85 x 0.44/80 = 0.00158 gallon

For 1 revolution the fuel taken =   0.00158 gallon

Now 1 gallon = 3785.41 ml

so 0.00158 gallon = 5.99 ml

As given 1 ml takes 20 drops then

5.99 ml will take around = 119.87 drops ~ 120 drops